Module 5: Advanced Mechanics
NSW HSC Physics Year 12
Module Overview
Advanced Mechanics builds on the foundational mechanics concepts from Year 11, extending into projectile motion, circular motion, and gravitational physics. This module prepares students for understanding orbital mechanics, satellite motion, and the broader implications of Newton’s Law of Universal Gravitation.
Indicative Hours: 30 hours
Related Outcomes:
- PH12-4 selects and processes appropriate qualitative and quantitative data and information using a range of appropriate media
- PH12-5 analyses and evaluates primary and secondary data and information
- PH12-12 describes and analyses qualitatively and quantitatively circular motion and motion in a gravitational field, in particular, the projectile motion of particles
Inquiry Questions
This module addresses the following inquiry questions:
How can models that are used to explain projectile motion be used to analyse and make predictions?
Why do objects move in circles?
How does the force of gravity determine the motion of planets and satellites?
How is energy transferred and transformed in motion in gravitational fields?
Key Concepts
5.1 Projectile Motion
Analyse projectile motion by treating horizontal and vertical components independently.
Content:
- Analyse the motion of projectiles by resolving motion into horizontal and vertical components
- Calculate range, time of flight, and maximum height using kinematic equations
- Apply vector analysis to projectile motion problems
- Investigate factors affecting projectile motion experimentally
Key Formulas:
| Quantity | Formula |
|---|---|
| Horizontal displacement | \(x = v_x t\) |
| Vertical displacement | \(y = v_{y0}t - \frac{1}{2}gt^2\) |
| Time of flight | \(T = \frac{2v_0\sin\theta}{g}\) |
| Range | \(R = \frac{v_0^2\sin(2\theta)}{g}\) |
| Maximum height | \(H = \frac{v_0^2\sin^2\theta}{2g}\) |
5.2 Circular Motion
Understand uniform circular motion and the forces that cause objects to move in circular paths.
Content:
- Define uniform circular motion and centripetal acceleration
- Apply Newton’s laws to analyse circular motion
- Calculate centripetal force and its relationship to mass, velocity, and radius
- Investigate the forces acting on objects in horizontal and vertical circular motion
Key Formulas:
| Quantity | Formula |
|---|---|
| Angular velocity | \(\omega = \frac{2\pi}{T} = 2\pi f\) |
| Centripetal acceleration | \(a_c = \frac{v^2}{r} = \omega^2 r\) |
| Centripetal force | \(F_c = \frac{mv^2}{r} = m\omega^2 r\) |
| Period | \(T = \frac{2\pi r}{v}\) |
5.3 Motion in Gravitational Fields
Apply Newton’s Law of Universal Gravitation to predict orbital motion and satellite mechanics.
Content:
- Apply Newton’s Law of Universal Gravitation to calculate gravitational field strength
- Derive and apply orbital velocity and period formulas
- Analyse satellite motion including geostationary orbits
- Calculate escape velocity and understand energy in gravitational fields
Key Formulas:
| Quantity | Formula |
|---|---|
| Gravitational force | \(F = \frac{Gm_1m_2}{r^2}\) |
| Gravitational field strength | \(g = \frac{GM}{r^2}\) |
| Orbital velocity | \(v = \sqrt{\frac{GM}{r}}\) |
| Orbital period | \(T = 2\pi\sqrt{\frac{r^3}{GM}}\) |
| Escape velocity | \(v_{esc} = \sqrt{\frac{2GM}{r}}\) |
| Gravitational potential energy | \(U = -\frac{Gm_1m_2}{r}\) |
Working Scientifically
Practical Investigations
- Projectile Motion Investigation
- Investigate factors affecting projectile range (launch angle, initial velocity)
- Analyse video footage of projectile motion to verify kinematic predictions
- Circular Motion Demonstration
- Investigate the relationship between centripetal force, mass, velocity, and radius
- Use rotating apparatus to measure centripetal acceleration
- Gravitational Field Modelling
- Use computer simulations to model orbital motion
- Analyse real satellite data to verify Kepler’s laws
HSC Exam Coverage
Module 5 concepts appear consistently in HSC Physics examinations, particularly in extended response questions involving calculations and explanations of orbital mechanics.
Common Question Types:
- Projectile motion calculations (range, time, height)
- Circular motion force analysis
- Satellite orbit calculations
- Energy transformations in gravitational fields
- Comparative analysis of orbital parameters
Recent HSC Questions:
| Year | Question | Topic | Marks |
|---|---|---|---|
| 2024 | Q25 | Gravitational fields | 7 |
| 2024 | Q31 | Orbital mechanics | 6 |
| 2023 | Q27 | Projectile motion | 5 |
| 2023 | Q32 | Satellite orbits | 8 |
Practice Resources
Multiple Choice Practice
Extended Response Practice
Key Definitions
- Projectile
- An object moving freely under the influence of gravity alone, with no propulsion.
- Centripetal Force
- The net force directed toward the centre of a circular path that causes an object to follow that path.
- Gravitational Field Strength
- The force per unit mass experienced by a small test mass placed in a gravitational field (N/kg or m/s²).
- Orbital Velocity
- The velocity required for an object to maintain a stable orbit at a given altitude.
- Escape Velocity
- The minimum velocity required for an object to escape from a gravitational field without further propulsion.
- Geostationary Orbit
- An orbit where a satellite remains above the same point on Earth’s surface, with a period of 24 hours.